I've noticed that some animations run smoother, specially those related to the status bar. I hide it with Nova launcher and it was always a bit jumpy, now transitions are better.

Most reports from Brazilian users indicate an improvement in battery life after the update. Right now I'm travelling and keep the phone on aeroplane mode with occasional WiFi connection, so I can't check if this is true.

Did it update from 6.0, or from Lollipop? If it updated from 6.0, was the SD card previously set as adoptable storage?

Regarding the battery, show us some battery stats. Charge up to 100%, then let it drain to 20-30% with normal usage, without charging in between. Then show us:

1. The main Settings>Battery screen.
2. The fullscreen battery graph screen (which shows Awake time and Cell Signal Strength).
3. The Screen category (to see total Screen On time).
4. The Cell Standby category, if present (to see Time Without Signal).